This short note considers Hessian updates for a sequential quadratically constrained quadratic programming (SQCQP) method. The SQCQP method is an iterative method to solve an inequality constrained optimization problem. At each iteration, the SQCQP method solves a quadratically constrained quadratic programming subproblem whose objective function and constraints are approximations to the object...

We consider the problem of the global convergence of gradient-based optimization algorithms for interstitial high-dose-rate (HDR) brachytherapy dose optimization using variance-based objectives. Possible local minima could lead to only sub-optimal solutions. We perform a configuration space analysis using a representative set of the entire non-dominated solution space. A set of three prostate i...

We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special structure of the exact penalty problem, we propose a decomposition method that can seek a global optimal solution of the zero-norm minimizatio...

The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis's nonsparse symmetrization formula derived. A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed. The sparse BFGS generated by this method...

The standard formulations of the Kalman filter (KF) and extended Kalman filter (EKF) require storing and multiplication of matrices of size n×n, where n is the size of the state space, and the inversion of matrices of size m×m, where m is the size of the observation space. For large dimensions implementation issues arise. In this paper we introduce a Variational Kalman Filter (VKF) method to pr...

Energy minimization plays an important role in structure determination and analysis of proteins, peptides and other organic molecules; therefore, development of efficient minimization algorithms is important. Recently Morales and Nocedal have developed enriched methods for large scale unconstrained optimization that interlace iterations of the limited memory BFGS method (L-BFGS) and the Hessian...

Energy minimization plays an important role in structure determination and analysis of proteins, peptides, and other organic molecules; therefore, development of efficient minimization algorithms is important. Recently, Morales and Nocedal developed hybrid methods for large-scale unconstrained optimization that interlace iterations of the limited-memory BFGS method (L-BFGS) and the Hessian-free...

The current work focuses on the development and application of an efficient algorithm for optimization of threedimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or large-eddy simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a da...

We compare the performance of several robust large-scale minimization algorithms for the unconstrained minimization of an ill-posed inverse problem. The parabolized Navier–Stokes equation model was used for adjoint parameter estimation. The methods compared consist of three versions of nonlinear conjugate-gradient (CG) method, quasiNewton Broyden–Fletcher–Goldfarb–Shanno (BFGS), the limited-mem...